Question

A particle of charge q, mass m and energy E has de-Broglie wavelength `lambda.` For a particle of charge 2q, mass 2m and energy 2E, the de-Broglie wavelength is ____________.

Options

• `lambda/4`

• `2 lambda`

• `8 lambda`

• `lambda/2`

Answer 1

A particle of charge q, mass m and energy E has de-Broglie wavelength `lambda.` For a particle of charge 2q, mass 2m and energy 2E, the de-Broglie wavelength is `lambda/2`.

Explanation:

For any charged particle, de-Broglie wavelength is,

`lambda = "h"/sqrt(2"mE")`

`therefore lambda_2 = "h"/sqrt(2(2"m")(2"E"))`

`therefore lambda_2 = "h"/(2 xx sqrt(2"mE"))`

` = lambda/2`